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Number of subsets of proper divisors of numbers in A065218 summing to the number.
1

%I #21 Oct 12 2017 03:37:35

%S 0,1,2,5,7,10,34,278,751,2157,22208,676327,2225346,23259536,265050967,

%T 39161483067,70455119174849,776384598617893,133991542908557129,

%U 21819590324155207874,263763825614848727692,12883245190231409112736,661394651111310011564685

%N Number of subsets of proper divisors of numbers in A065218 summing to the number.

%C The numbers themselves are in A065218.

%F a(n) = A065205(A065218(n)).

%e Proper divisors of 12 are {1, 2, 3, 4, 6}. Two subsets of this sum to 12: {2, 4, 6} and {1, 2, 3, 6} - more than any smaller number, so 2 is in the sequence (and 12 is in A065218).

%t Union@ FoldList[Max, Array[Block[{dd = Most@ Divisors@ #, c, cc}, cc = Array[c, Length@ dd]; Length@{ ToRules[Reduce[And @@ (0 <= # <= 1 &) /@ cc && dd.cc == #, cc, Integers]]}] &, 360]] (* _Michael De Vlieger_, Oct 01 2017, after Jean-François Alcover at A065205 *)

%Y Cf. A065218, A064771, A063205, A005835, A002182, A004394.

%K nonn

%O 1,3

%A _Jud McCranie_, Oct 21 2001

%E Extended by _Max Alekseyev_, May 29 2009

%E Initial 0 prepended and offset corrected by _Amiram Eldar_, Oct 01 2017